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Massive Open Online Cours on Evolution Equations

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Written by Daouda Niang Diatta

Massive Open Online Cours on Evolution Equations

This Massive Open Online Course (MOOC) hase been designed and taught by :Diaraf SECK, full professor at University Cheikh Anta Diop of Dakar in Senegal and Lead researcher of the project NLAGA funded by the Simons Foundation And Cedric VILLANI, Fields medal in 2010, full professor at Université de Lyon I in France and Director Institut Henri Poincaré (IHP) (Paris), France.

The fees of the MOOC have been supported by the University Cheikh Anta Diop of Dakar (Senegal), the Institute Henri Poincaré (Paris, France), the University Pierre et Marie Curie (Paris, France), the University Sorbone (Paris France) and the University Claude Bernard of Lyon (France).

This MOOC is and will be very useful, for a lot of students and PhD students not belonging necessarily to NLAGA Project. It can be used by all PhD students from the Task 1 to the Task 8 of the NLAGA Project.

The aim is to produce a course and lecture notes from the master level to the PhD level on the topic of evolutions equations : the Ordinary Differential Equations (ODE) and Partial Differential Equations (PDE).

It is a project which the realization is in progress. And the first part of a series of courses on evolution équations is devoted to ODE and an introduction to Hamiltonian systems. Actually this course introduces the listener to the theory of differential equations. The ordinary differential equations are of universal use today, in all the sciences and in the industry. This course will help familiarize them with their language and theory, and to control the main techniques of qualitative study (behavior in time large, stability, approximation ... ). It is also a preparation for a course in partial differential equations, which are among the mathematical tools the most important and multifaceted of the contemporary world.

The course was started by a perspective on evolution equations, and then focused on the ordinary differential equations. It covered the following topics: local study, existence and uniqueness, qualitative study of the long-term behavior, introduction to modeling.